Physics-Informed Antisymmetric Recurrent Neural Networks with Initializer Network for Solving Nonlinear Time-Dependent Partial Differential Equations

Physics-informed neural network (PINN) is a machine learning-based approach for solving partial differential equations (PDEs). This paradigm leverages the system's prior knowledge in the form of PDE, as a regularization term to guide the training of the network. Traditionally, PINN relies on multilayer perceptrons (MLPs) to approximate the solution of PDEs. While this network's architecture has shown significant progress, PINN based on MLPs encounter several limitations for time-dependent PDEs, in particular for the temporal solutions. In addition, PINN is known to cope only with a fixed initial condition, which is a major drawback. In this work, we propose Physics-Informed Antisymmetric Recurrent Neural Network (PIARNN), which employs an initializer network, to solve time-dependent PDEs with various initial conditions. The recurrent connections are parameterized with a strictly upper-triangular parameter vector, which enforces a stable learning. PDEBench dataset is used to conduct experiments on reaction-diffusion and Burger's equations. It was observed that the proposed method can achieve competitive performance compared to the state-of-the-art methods such as conventional PINN, U-Net and Fourier neural operator (FNO).